In perturbative calculations of physical processes, there appear at higher orders ultraviolet divergences, which require a procedure (called the renormalization scheme) for their subtraction.
At finite order in perturbation theory, a number of ambiguities occur as the renormalization procedure is not uniquely specified and, in particular,
amplitudes calculated in perturbation theory appear to depend on an arbitrary renormalization scale (usually denoted by \(\mu \) ).
However, since these amplitudes are connected to physical observables, these cannot depend on such a parameter
(or any other parameter that characterize the renormalization scheme).
This can be achieved if the coupling becomes a function of \(\mu \) , which leads to the independence of observables on the choice of this scale parameter. The renormalization group (RG) is closely related to the scale invariance of physical systems.
Furthermore, it
improves the properties of the perturbative series in the ultraviolet region, by summing the radiative corrections that occur in higher orders of perturbation theory [1]}, [2]}, [3]}, [4]}, [5]}, [6]}. Due to asymptotic freedom [7]}, physical quantities in QCD at high momentum squared \(Q^2\)  can be evaluated by solving the RG equations in terms of a power series involving the perturbative running coupling \(\alpha (Q^2)\) .
